What are the divisors of 5348?

1, 2, 4, 7, 14, 28, 191, 382, 764, 1337, 2674, 5348

There is a total of 12 positive divisors.
The sum of these divisors is 10752.
The arithmetic mean is 896.

8 even divisors

2, 4, 14, 28, 382, 764, 2674, 5348

4 odd divisors

1, 7, 191, 1337

How to compute the divisors of 5348?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5348 by each of the numbers from 1 to 5348 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5348 / 1 = 5348 (the remainder is 0, so 1 is a divisor of 5348)
5348 / 2 = 2674 (the remainder is 0, so 2 is a divisor of 5348)
5348 / 3 = 1782.6666666667 (the remainder is 2, so 3 is not a divisor of 5348)
...
5348 / 5347 = 1.0001870207593 (the remainder is 1, so 5347 is not a divisor of 5348)
5348 / 5348 = 1 (the remainder is 0, so 5348 is a divisor of 5348)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5348 (i.e. 73.130021195129). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5348 / 1 = 5348 (the remainder is 0, so 1 and 5348 are divisors of 5348)
5348 / 2 = 2674 (the remainder is 0, so 2 and 2674 are divisors of 5348)
5348 / 3 = 1782.6666666667 (the remainder is 2, so 3 is not a divisor of 5348)
...
5348 / 72 = 74.277777777778 (the remainder is 20, so 72 is not a divisor of 5348)
5348 / 73 = 73.260273972603 (the remainder is 19, so 73 is not a divisor of 5348)